Results 11 to 20 of about 552 (63)

On Quasi S‐Propermutable Subgroups of Finite Groups

Journal of Mathematics, Volume 2020, Issue 1, 2020., 2020
A subgroup H of a finite group G is said to be quasi S‐propermutable in G if K⊲¯G such that HK is S‐permutable in G and H ∩ K ≤ HqsG, where HqsG is the subgroup formed by all those subgroups of H which are S‐propermutable in G. In this paper, we give some generalizations of finite group G by using the properties and effects of quasi S‐propermutable ...
Hong Yang, Abid Mahboob, Asim Zafer, Iftikhar Ali, Zafar Ullah, Absar Ul Haq, Ji Gao   +6 more
wiley   +1 more source

On the commuting probability and supersolvability of finite groups [PDF]

, 2013
For a finite group $G$, let $d(G)$ denote the probability that a randomly chosen pair of elements of $G$ commute. We prove that if $d(G)>1/s$ for some integer $s>1$ and $G$ splits over an abelian normal nontrivial subgroup $N$, then $G$ has a nontrivial ...
Lescot, Paul, Nguyen, Hung Ngoc, Yang, Yong   +2 more
core   +2 more sources

The index complex of a maximal subalgebra of a Lie algebra. [PDF]

, 2010
Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M.
Beidleman, David A. Towers, Deskins, Mukherjee   +3 more
core   +2 more sources

Chains of modular elements and shellability [PDF]

, 2012
Let L be a lattice admitting a left-modular chain of length r, not necessarily maximal. We show that if either L is graded or the chain is modular, then the (r-2)-skeleton of L is vertex-decomposable (hence shellable).
Babson, Birkhoff, Björner, Björner, Björner, Brown, Duval, Forman, Hersh, Hersh, Jonsson, Jonsson, Kohler, Kozlov, Liu, McNamara, Provan, Russ Woodroofe, Sagan, Shareshian, Shareshian, Stanley, Stanley, Thomas, Thévenaz, Wachs, Wachs, Woodroofe, Woodroofe, Woodroofe   +29 more
core   +1 more source

List decoding group homomorphisms between supersolvable groups [PDF]

, 2014
We show that the set of homomorphisms between two supersolvable groups can be locally list decoded up to the minimum distance of the code, extending the results of Dinur et al who studied the case where the groups are abelian.
Guo, Alan, Sudan, Madhu
core   +3 more sources

A Note on the Normal Index and the c‐Section of Maximal Subgroups of a Finite Group

Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014
Let M be a maximal subgroup of finite group G. For each chief factor H/K of G such that K ≤ M and G = MH, we called the order of H/K the normal index of M and (M∩H)/K a section of M in G. Using the concepts of normal index and c‐section, we obtain some new characterizations of p‐solvable, 2‐supersolvable, and p‐nilpotent.
Na Tang, Xianhua Li, Junjie Wei
wiley   +1 more source

Finite Groups with Some SE‐Supplemented Subgroups

Algebra, Volume 2013, Issue 1, 2013., 2013
Let H be a subgroup of a finite group G, p a prime dividing the order of G, and P a Sylow p‐subgroup of G for prime p. We say that H is SE‐supplemented in G if there is a subgroup K of G such that G = HK and H∩K ≤ HseG, where HseG denotes the subgroup of H generated by all those subgroups of H which are S‐quasinormally embedded in G.
Guo Zhong, Liying Yang, Huaquan Wei, Xuanlong Ma, Jiayi Xia, Antonio M. Cegarra   +5 more
wiley   +1 more source

Finite Groups Whose Certain Subgroups of Prime Power Order Are S‐Semipermutable

International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011
Let G be a finite group. A subgroup H of G is said to be S‐semipermutable in G if H permutes with every Sylow p‐subgroup of G with (p, |H|) = 1. In this paper, we study the influence of S‐permutability property of certain abelian subgroups of prime power order of a finite group on its structure.
Mustafa Obaid, A. Kiliçman
wiley   +1 more source

Mutually Permutable Products of Finite Groups

International Scholarly Research Notices, Volume 2011, Issue 1, 2011., 2011
Let G be a finite group and G1, G2 are two subgroups of G. We say that G1 and G2 are mutually permutable if G1 is permutable with every subgroup of G2 and G2 is permutable with every subgroup of G1. We prove that if G = G1G2 = G1G3 = G2G3 is the product of three supersolvable subgroups G1, G2, and G3, where Gi and Gj are mutually permutable for all i ...
Rola A. Hijazi, M. Asaad, G. Buskes, G. Mason, L. Vinet   +4 more
wiley   +1 more source

A note on p‐solvable and solvable finite groups

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 4, Page 821-824, 1994., 1994
The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p‐solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p‐solvable and normal solvable subgroups, respectively, of G.
R. Khazal, N. P. Mukherjee
wiley   +1 more source